Hi guys, it's me Teacher Gon. In today's video, we will talk about solving quadratic equations by factoring. Solving quadratic equations by factoring is one of the methods on how to get the solution of any quadratic equations. So without further ado, let's do this topic.
For this video, I will give you six different quadratic equations for us to solve or for us to get what are the solutions of each quadratic equation. We have here, solve the following quadratic equations by factoring. Here's the first question. We have 3x squared minus 9x is equal to 0. Number 2, 5x squared minus 20x is equal to 2, is equal to 0. These first two equations can be factored or can be solved by factoring.
And to be specific, we will use common monomial factoring here. So what we have here is 3x squared minus 9x. So what we will do here is that you will know or you need to think what is common between the numbers of each term and in the variable in each term. Here we have 3 and 3 as the coefficient.
Knowing that the numbers are 3 and 9, meaning which is common is a factor of 3. So we have here our CMF or common polynomial factor 3. for the numbers and for the variable as you can see the two terms yung two terms natin meron siyang parehas na x meaning which is common is also x so the common monomial factor of this equation is 3x ito yung yung factor natin sa labas we have 3x now to get the other factor yung gawin mo lang to divide mo daw by 3x so 3x squared divided by 3x is x And this one divided by 3x. 9x divided by 3x is equal to 3. And then copy the negative sign. So you have here the factors are as 3x times x minus 3 is equal to 0. What's next after factoring in solving quadratic equations, we need to equate each factor by 0. The first factor is 3x.
So that is 3x. is equal to zero. While the other factor is x minus three, you need also to equate this by zero. Solve for x, divide both sides by three, divide by three, cancel, cancel. Your x here is equal to zero.
This is the first value of x in the given equation. Next, let's continue. We have x minus three.
So for x transpose this to the other side you have x is equal to positive 3 and this is now the second value of x. So what we have here are the solutions of the first equation x is equal to 0 and x is equal to 3. Now let's continue with item number 2. For number 2 same thing we need to do is to get the common monomial factor. What is common between the numbers?
5 and negative 20, common is 5. As for the variables, the common is x, meaning the first factor is 5x. What about the second factor? Divide both sides by 5x, by 5x. This is x, and this one, negative 20x divided by 5x is minus 4, is equal to 0. Your two factors equate by 0. 5x is equal to 0. The other is x minus 4 is equal to 0. Divide both sides by 5. Cancel. x is equal to 0. This is the first value of x.
Next, solve this. Transpose to the other side. x is equal to from negative. It will become positive 4. And as you can see, we have now are the values of x. Now in our next part of our video, I will give you example number 3 and number 4 and these are the given equations.
So what we have here is x squared minus 16 is equal to 0. Now, we have a pattern in factoring this kind of example. This one is under difference of two squares. Our pattern here is this. You have a squared minus b squared.
And if you want to factor this kind of expression, that would be a plus b times times a minus b first thing you need to do get the square root of x squared because that would be your a square root of x squared is x square root of 16 is 4 and this is your a and b copy plus x minus 4 and then equal to 0 you only need to use this pattern guys then equate each factor x plus 4 is equal to 0 the other is x minus 4 is equal to 0 transpose to the other side x from positive 4 minus 4 this is it guys second factor transpose it to the other side from negative it will become positive this x is equal to positive 4 and Here are the values of x. We have negative 4 and positive 4. Now you can pause the video for a while and you can try to factor this kind of equation and solve for the value of x. I'll wait for you. Okay, so for this kind of equation x squared minus 64 is equal to 0, create two parentheses, x equal to 0. Square root of x squared is x. Square root of 64 is 8. Plus minus.
Sir, can we interchange the sign? Yes. Possible yan.
Equate each factor by 0. x plus 8 is equal to 0. x minus 8 is equal to 0. Transpose this. It will become x is equal to... What?
Negative 8. Now for the other factor, for the other equation, we have x minus 8 is equal to 0. Simply transpose negative 8 and it will become x is equal to positive 8. So as you can see, these are the values of x negative 8 and 8 as the solution of x squared minus 64. Now for our third case, I will give you a trinomial quadratic equation. For those of you who are not familiar with this kind of equation, We can solve this by factoring again. First, you will create two parentheses here. And let's figure out what are the factors.
By the way, you can do this easily if the coefficient of the quadratic term is simply 1. Now, let's figure out a factor of 15 wherein when you add them, the sum is negative 8. Since this one is negative and this is positive, we will assume that the factors must be both negatives. So the factors of 15 are 15 times 1. We can use negative, negative. Another possible factor are... Negative 5 times negative 3. So among these factors, which of these is correct, guys?
We will choose negative 5 and negative 3 because it will add up to negative 8. Let's check. Negative 5 times negative 3 is positive 15. Negative 5 plus negative 3 is positive 8. So the factors are x minus 5. and x minus 3. Equate each factor by 0. x minus 5 is equal to 0. The other is x minus 3 is equal to 0. Transpose this to the other side. You have your x is equal to 5. On the other side, transpose negative 3. It will become positive x is equal to positive 3. As easy as that, guys.
Now let's continue with number 6. For number 6, we are given x squared minus 7x plus 12. Same scenario, the constant here is positive while the middle term or the coefficient of the linear term is negative, meaning we're trying to get two negative integers as our factor. The factors of 12 are negative 12 times negative 1. Possible, negative 6 times negative 2, then negative 4 times negative 3. So among these three pairs of factors, the correct answer is negative 4 and negative 3 because it will add up to negative 7. Let's create a factor, x minus 4, x minus 3 is equal to 0. Equate each equation. x minus 4 is equal to 0. x minus 3 is equal to 0. Transpose.
Transpose. Here, x is equal to positive 4. Here, x is equal to positive 3. And that's it, guys. Now, guys, as our routine in our tutorial videos, I will give you a problem, and I want you to solve it. And please comment down below what are the values of x of these quadratic equations.
Number one, x squared minus 100 is equal to zero. For number two, x squared plus 5x plus 6 is equal to zero. And again guys, if you're new to my channel...
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Bye-bye!